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You have 2 coins. One is a fair coin. The other flips heads 100% of the time. You took one of the coins. You took a completely random one, so it's a 50/50 chance for both of them. You flip the coin you took. It flips heads. What is the chance the next time you flip that same coin, it flips heads again?
You start by flipping a coin twice. If they are both heads, you stop. If not, you flip another coin. If the last 2 you flipped were heads, you stop. You keep flipping another coin and checking if the last 2 you flipped were heads. What is the EV (expected value) of the number of times you flip the coin?
What is the derivative of x(yᶻ)?